(* ::Package:: *)

 


(* ::Section:: *)
(* SumT *)


(* ::Text:: *)
(*`SumT[1, m]` is the alternative harmonic number $\sum _{i=1}^m (-1){}^{\wedge}i/i$ *)


(* ::Text:: *)
(*`SumT[r, n]` represents `Sum[(-1)^i/i^r, {i,1,n}]`*)


(* ::Text:: *)
(*`SumT[r,s, n]` is `Sum[1/k^r (-1)^j/j^s, {k, 1, n}, {j, 1, k}]`.*)


(* ::Subsection:: *)
(* See also *)


(* ::Text:: *)
(*SumP, SumS.*)


(* ::Subsection:: *)
(* Examples *)


SumT[1,m-1]


SumT[2,m-1]


SumT[1,m]


SumT[1,m,Reduce->True]


SumT[1,4]


SumT[1,2,m-1]


SumT[1,2,42]


SumT[1,4]


SumS[-1,4]


SumT[1,2,12]


SumS[1,-2,42]


Array[SumT,6]


Array[SumS[-2,1,#1]&,6]
